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S17: Introduction to Numerical Methods. TT 2008 Lecture 1 Numerical aspects of computing. Reasons to study. “Solve” problems with no analytic solution Non-linear equations Complex behaviors Understand these methods Gain familiarity with common algorithms
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S17: Introduction toNumerical Methods TT 2008 Lecture 1 Numerical aspects of computing
Reasons to study • “Solve” problems with no analytic solution • Non-linear equations • Complex behaviors • Understand these methods • Gain familiarity with common algorithms • Computing realities and calculations in principle • How they can be improved • How they can fail • Numerical methods shouldn’t be used blindly
Introduction, numerical aspects of computing Finding roots of equations Curve fitting Matrix algebra Eigensystems Numerical integration Fourier series Ordinary differential equations Partial differential equations Monte Carlo methods Monte Carlo integration Homework and revision Course outline
Lectures • Week 1: W Th F 2pm • Week 2: W Th F 2pm • Week 3: no lectures • Week 4: Th F 2pm (no Wednesday) • Week 5: W Th F 2pm
Resources • http://www-pnp.physics.ox.ac.uk/~tseng/teaching/s17/index.html • My main resource: R.L. Burden, J.D. Faires, Numerical Methods, 3rd ed., Boston: Prindle, Weber & Schmidt, 1985. • More mathematical: S.D. Conte, Carl de Boor, Elementary Numerical Analysis: An Algorithmic Approach, New York: McGraw-Hill, 1980. • Koonin and Meredith, Computational Physics • Kalos and Whitlock, Monte Carlo Methods, vol. 1. • Veterling, Numerical Recipes • Devroye, Non-Uniform Random Variate Generation http://cg.scs.carleton.ca/~luc/rnbookindex.html • http://www-teaching.physics.ox.ac.uk/computing/NumericalMethods/nummethods.html • Lecture notes from 2005 • Online courses • Problem sets (will be augmented occasionally)
Next lecture • Thursday 2pm, same location • Solving non-linear equations